The argument from incredulity is a logical fallacy that essentially relies on a lack of imagination in the audience.

The general form of the argument is as follows.

Minor premise: One can't imagine (or has not imagined) how P could be so.

Major premise (unstated): If P, then one could imagine (or would have imagined) how P could be so.

Conclusion: Not-P.

As a syllogism this is valid. The fallacy lies in the unstated major premise. If a state of affairs is impossible to imagine, it doesn't follow that it is false; it may only mean that imagination is limited. Moreover, if no one has yet managed to imagine how a state of affairs is possible, it doesn't follow that no one will ever be able to.

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As an example, creationists incessantly use some difficult-to-explain facet of biology as "proof" of a creator. The problem is that, though there is no non-design explanation for how precisely a certain organ could have evolved at the moment, one may be discovered in the future. Contrary to the instincts of many creationists, lack of an explanation does not justify confecting whatever explanation one would prefer. The inexplicable is just that, and does not justify speculation as proof.

Sometimes creationists compute the astronomical odds against a molecule having a certain structure from the simple probability of n atoms arranging themselves so. They gloss over the fact that chemical laws trim most of the extraneous possibilities away. For instance, there are many ways to theoretically arrange hydrogen atoms and oxygen atoms in a molecule, but in reality, most of what forms is H2O. Note that the creationist's fundamental error is not his ignorance of this fact, but his assumption that there is nothing more to know.

Another example is a scientific explanation of personal phenomenal experiences or "qualia". Because they do not know how physical processes could produce qualia, many philosophers conclude that therefore qualia cannot ever be explained.

Another form, the argument from personal incredulity, takes the form "I can't believe P, therefore not-P." Merely because one cannot believe that, for example, homeopathy is no more than a placebo does not magically make such treatment effective. Clinical trials are deliberately designed in such a way that an individual personal experience is not important compared to data in aggregate. Human beings have extremely advanced pattern recognition skills, to the extent that they are objectively poor judges of probability.

Sometimes argument from incredulity is applied to epistemological statements, taking the form "One can't imagine how one could know whether P or not-P, therefore it is unknowable whether P or not-P." This is employed by some (though not all) strong agnostics who say it is unknowable whether gods exist. The argument in this case is, "No one has thought of a way to determine whether there are gods, so there is no way." The implied major premise, "If there were such a way, someone would have thought of it," is disputable.